import numpy as np
import random as rd

from ipywidgets import interact, interactive, fixed, interact_manual
from ipywidgets import FloatSlider

from bokeh.io import push_notebook, show, output_notebook
from bokeh.layouts import row, column
from bokeh.models import CustomJS, Slider, Arrow, Label, ArrowHead
from bokeh.plotting import figure, output_file, show, ColumnDataSource, output_notebook
output_notebook()

n = 500
x = np.linspace(0, 20, n)
y = np.linspace(0, 20, n)
r = np.sqrt(x**2 + y**2)

rot_matrix = np.array([[np.cos(0.5*np.pi), -np.sin(0.5*np.pi)], 
                       [np.sin(0.5*np.pi), np.cos(0.5*np.pi)]])

# Unit vectors points for each coordinate
zeros = np.zeros(n)
u = np.linspace(0, 5, n)
u_theta = np.dot(np.array([5, 5]), rot_matrix)

plot = figure(x_range=(-50, 50), y_range=(-50, 50), width=600, height=600, title="Polar coordinate")

# Main line
line = plot.line(x, y, color="#00ced1", line_width=5, alpha=0.6, legend_label="Transformation linéaire")

# Labels for coordinates
x_text = f"x = {x[-1]:.2f}"
y_text = f"y = {y[-1]:.2f}"
x_label = Label(x=x[-1], y=0, text=x_text)
y_label = Label(x=0, y=y[-1], text=y_text)

# Unit vectors lines with labels
plot.line(u, zeros, color="#ED192D", line_width=3, alpha=0.5, legend_label="Vector unité sur l'axe x")
u_x_label = Label(x=u[-1], y=0, text='u_x')

plot.line(zeros, u, color="#ED192D", line_width=3, alpha=0.5, legend_label="Vector unité sur l'axe y")
u_y_label = Label(x=0, y=u[-1], text='u_y')

u_r_line = plot.line(x[-1]+u, y[-1]+u, color="#008000", line_width=3, alpha=0.5, legend_label="Vector unité de rho")
u_r_label = Label(x=x[-1]+u[-1], y=y[-1]+u[-1], text='u_r')
u_theta_line = plot.line(x[-1]+np.linspace(0, u_theta[0], n), y[-1]+np.linspace(0, u_theta[1], n), color="#008000", line_width=3, alpha=0.5, legend_label="Vector unité de theta")
u_theta_label = Label(x=x[-1]+u_theta[0], y=y[-1]+u_theta[1], text='u_theta')

# Plot properties
plot.xaxis.axis_label = 'x axis'
plot.yaxis.axis_label = 'y axis'
plot.legend.background_fill_alpha = 0.2

# Add layout to the plot
plot.add_layout(x_label)
plot.add_layout(y_label)
plot.add_layout(u_x_label)
plot.add_layout(u_y_label)
plot.add_layout(u_r_label)
plot.add_layout(u_theta_label)

def update_plot(r_slider, theta_slider):
    M_x = r_slider*np.cos(theta_slider)
    M_y = r_slider*np.sin(theta_slider)
    
    u_r = np.array([5* np.cos(theta_slider), 5*np.sin(theta_slider)])
    #Rotate the unit vector for theta
    theta_up = -np.dot(u_r.T, rot_matrix)
    
    line.data_source.data['x'] = np.linspace(0, M_x, n)
    line.data_source.data['y'] = np.linspace(0, M_y, n)
    x_label.x = M_x
    x_label.text = "x = " + "%.2f" % round(M_x,2)
    y_label.y = M_y
    y_label.text = "y = " + "%.2f" % round(M_y,2)

    
    #Unit vectors update
    u_r_line.data_source.data['x'] = np.linspace(0, u_r[0], n) + M_x
    u_r_line.data_source.data['y'] = np.linspace(0, u_r[1], n) + M_y
    
    
    u_theta_line.data_source.data['x'] = np.linspace(0, theta_up[0], n) + M_x
    u_theta_line.data_source.data['y'] =np.linspace(0, theta_up[1], n) + M_y
    
    u_r_label.x = u_r[0] + M_x
    u_r_label.y = u_r[1] + M_y
    u_theta_label.x = theta_up[0] + M_x
    u_theta_label.y = theta_up[1] + M_y
    
    push_notebook()
    return

show(plot, notebook_handle=True)
interact(update_plot, \
         r_slider = FloatSlider(min=0.0, max=r[-1] + 5, step=0.5, value=20, description='rho :'), \
         theta_slider = FloatSlider(min=0.0, max=2*np.pi + 0.05, step=0.05, value=0.5, description='theta :'));

interactive(children=(FloatSlider(value=20.0, description='rho :', max=33.2842712474619, step=0.5), FloatSlide…

Important note¶

Lien entre coordonnées polaires et coordonnées cartésiennes¶